# Complex Variables

## Stephen D. Fisher

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Hundreds of solved examples, exercises, and applications help students gain a firm understanding of the most important topics in the theory and applications of complex variables. Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, and transform methods. 1990 edition. Appendices.

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Contenuti:

1. The complex plane 1.1 The complex numbers and the complex plane 1.1.1 A formal view of the complex numbers 1.2 Some geometry 1.3 Subsets of the plane 1.4 Functions and limits 1.5 The exponential, logarithm, and trigonometric functions 1.6 Line integrals and Green's theorem 2. Basic properties of analytic functions 2.1 Analytic and harmonic functions; the Cauchy-Riemann equations 2.1.1 Flows, fields, and analytic functions 2.2 Power series 2.3 Cauchy's theorem and Cauchy's formula 2.3.1 The Cauchy-Goursat theorem 2.4 Consequences of Cauchy's formula 2.5 Isolated singularities 2.6 The residue theorem and its application to the evaluation of definite integrals 3. Analytic functions as mappings 3.1 The zeros of an analytic function 3.1.1 The stability of solutions of a system of linear differential equations 3.2 Maximum modulus and mean value 3.3 Linear fractional transformations 3.4 Conformal mapping 3.4.1 Conformal mapping and flows 3.5 The Riemann mapping theorem and Schwarz-Christoffel transformations 4. Analytic and harmonic functions in applications 4.1 Harmonic functions 4.2 Harmonic functions as solutions to physical problems 4.3 Integral representations of harmonic functions 4.4 Boundary-value problems 4.5 Impulse functions and the Green's function of a domain 5. Transform methods 5.1 The Fourier transform: basic properties 5.2 Formulas Relating u and û 5.3 The Laplace transform 5.4 Applications of the Laplace transform to differential equations 5.5 The Z-Transform 5.5.1 The stability of a discrete linear system Appendix 1. The stability of a discrete linear system Appendix 2. A Table of Conformal Mappings Appendix 3. A Table of Laplace Transforms Solutions to Odd-Numbered Exercises Index

Sinossi:

Book by Fisher Stephen D

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## 1.Complex Variables: Second Edition

ISBN 10: 0486406792 ISBN 13: 9780486406794
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Descrizione libro 1999. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Codice libro della libreria V0-9780486406794

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## 2.Complex Variables Format: Trade Paper

Editore: Dover Publishers
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Descrizione libro Dover Publishers. Condizione libro: New. Brand New. Codice libro della libreria 0486406792

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## 3.Complex Variables (Paperback)

Editore: Dover Publications Inc., United States (1999)
ISBN 10: 0486406792 ISBN 13: 9780486406794
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Descrizione libro Dover Publications Inc., United States, 1999. Paperback. Condizione libro: New. New ed of 2 Revised ed. 229 x 165 mm. Language: English . Brand New Book. The most important topics in the theory and application of complex variables receive a thorough, coherent treatment in this introductory text. Intended for undergraduates or graduate students in science, mathematics, and engineering, this volume features hundreds of solved examples, exercises, and applications designed to foster a complete understanding of complex variables as well as an appreciation of their mathematical beauty and elegance. Prerequisites are minimal; a three-semester course in calculus will suffice to prepare students for discussions of these topics: the complex plane, basic properties of analytic functions (including a rewritten and reorganized discussion of Cauchy s Theorem), analytic functions as mappings, analytic and harmonic functions in applications, and transform methods. Useful appendixes include tables of conformal mappings and Laplace transforms, as well as solutions to odd-numbered exercises. Students and teachers alike will find this volume, with its well-organized text and clear, concise proofs, an outstanding introduction to the intricacies of complex variables. Codice libro della libreria AAC9780486406794

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## 4.Complex Variables (Paperback)

Editore: Dover Publications Inc., United States (1999)
ISBN 10: 0486406792 ISBN 13: 9780486406794
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Descrizione libro Dover Publications Inc., United States, 1999. Paperback. Condizione libro: New. New ed of 2 Revised ed. 229 x 165 mm. Language: English . Brand New Book. The most important topics in the theory and application of complex variables receive a thorough, coherent treatment in this introductory text. Intended for undergraduates or graduate students in science, mathematics, and engineering, this volume features hundreds of solved examples, exercises, and applications designed to foster a complete understanding of complex variables as well as an appreciation of their mathematical beauty and elegance. Prerequisites are minimal; a three-semester course in calculus will suffice to prepare students for discussions of these topics: the complex plane, basic properties of analytic functions (including a rewritten and reorganized discussion of Cauchy s Theorem), analytic functions as mappings, analytic and harmonic functions in applications, and transform methods. Useful appendixes include tables of conformal mappings and Laplace transforms, as well as solutions to odd-numbered exercises. Students and teachers alike will find this volume, with its well-organized text and clear, concise proofs, an outstanding introduction to the intricacies of complex variables. Codice libro della libreria AAC9780486406794

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## 5.Complex Variables: Second Edition (Paperback)

ISBN 10: 0486406792 ISBN 13: 9780486406794
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Descrizione libro Paperback. Condizione libro: New. 2nd. 165mm x 25mm x 234mm. Paperback. Hundreds of solved examples, exercises, and applications help students gain a firm understanding of the most important topics in the theory and applications of complex variables. Topics in.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 448 pages. 0.612. Codice libro della libreria 9780486406794

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## 6.Complex Variables: Second Edition

Editore: Dover Publications
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Descrizione libro Dover Publications. Paperback. Condizione libro: New. Paperback. 448 pages. Dimensions: 9.0in. x 6.5in. x 0.9in.Hundreds of solved examples, exercises, and applications help students gain a firm understanding of the most important topics in the theory and applications of complex variables. Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, and transform methods. Perfect for undergradsgrad students in science, mathematics, engineering. A three-semester course in calculus is sole prerequisite. 1990 edition. Appendices. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Codice libro della libreria 9780486406794

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## 7.Complex Variables: Second Edition (Dover Books on Mathematics)

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ISBN 10: 0486406792 ISBN 13: 9780486406794
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Descrizione libro Dover Publications, 1999. Paperback. Condizione libro: New. book. Codice libro della libreria 0486406792

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## 8.Complex Variables

Editore: Dover Publications Inc. 1999-10-29, New York (1999)
ISBN 10: 0486406792 ISBN 13: 9780486406794
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Descrizione libro Dover Publications Inc. 1999-10-29, New York, 1999. paperback. Condizione libro: New. Codice libro della libreria 9780486406794

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## 9.Complex Variables: Second Edition (Dover Books on Mathematics)

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Descrizione libro Dover Publications. PAPERBACK. Condizione libro: New. 0486406792 Special order direct from the distributor. Codice libro della libreria ING9780486406794

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## 10.Complex Variables: Second Edition (Dover Books on Mathematics)

Editore: Dover Publications (1999)
ISBN 10: 0486406792 ISBN 13: 9780486406794
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Descrizione libro Dover Publications, 1999. Paperback. Condizione libro: New. 2. Codice libro della libreria DADAX0486406792

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